My thoughts on the situation? Alright.
Basically, the whole problem is Ned's sense of honor. It's that simple. He's not stupid - not the brightest blade in the box, but he can put the pieces together alright when he needs to - he just isn't willing to do the smart thing when it is of questionable honor.
Despite all the unwise decisions made thus far he had at least three outs that he recognized and refused to take:
-Tell the King, as he's dying, about the situation. I would not be surprised if pure rage kept Robert alive long enough to order some serious hurt done to the Lannisters, enough to at least get them out of a position to have direct designs on the throne. The most violent option, but probably effective.
-Take Renly's suggestion and hold Joffrey hostage. Probably doable with minimal bloodshed, though it'd still be violent and cause some obvious strife, not to mention frightening the little ones with the whole abduction thing. If it were me in Ned's shoes, I'd probably go with this one, not because it's the best option but because it's the simplest and works in the very short term. I'm not even sure how this is dishonorable, honestly; I think he just didn't want to upset/hurt the children, which is commendable, but a very small concern compared with the good of the entire realm. As for whether Renly belongs on the throne? Ehh...that's another story, but... Option number three is probably the "best" option for results, but because it's more long term and devious Ned's not really cut out for success there.
-And what is that option? Littlefinger's, of course. Yes, he's a bitter prick and far too clever for his own good at times, but I got the feeling that if Ned had gone along with Petyr's plan then he'd have had the support of the gold cloaks as long as he didn't screw it up by suggesting some royal incest was going on in a public venue, for instance. Is it ideal? No, but it keeps everyone alive and the balance of power relatively unchanged, since Petyr's probably still more on Ned's side than Cersei's as long as Ned plays along with his ideas. How far could they manipulate circumstances to disfavor the Lannisters before it got ugly? Hard to say - making this possibly the best option or just as bad as what Ned actually did; it's too much a long-term plan to guess that far ahead how it might've turned out.
ANY of these options would've been better than openly declaring the truth in the court surrounded by armed men of dubious trustworthiness, the gallant fool.
As for the rest? Robert shouldn't have set a kill order on Daenerys in the first place for the reasons Ned stated early on, and whether or not he was drugged is irrelevant. If the boar hadn't killed him I'm sure some other "mishap" would've taken him out soon enough for basically the same scenario to play out as it did.